Magnetization of Flat Superconducting Films on Ferromagnetic Substrates

Ferromagnetic substrate influences the electromagnetic response of a type-II superconducting film to the applied magnetic field. We present a two-dimensional integrodifferential model for the magnetization of a flat superconductor/ferromagnet bilayer of an arbitrary shape using a thin shell quasistatic model for the ferromagnetic substrate and an infinitely thin approximation for the superconducting layer. An efficient numerical method is developed and used to investigate the effect of a ferromagnetic substrate. In particular, we simulate the thin bilayer magnetization in a parallel field and, for a high field, the critical-state distributions of the superconducting current density. These critical-state distributions are different from those known for a normal external field. Finally, we investigate the influence of a ferromagnetic substrate on superconducting film-based magnetic traps for cold atoms.